maintained by Forces of Double Frequency. 505 



maintaining influence. There is no mechanical force acting 

 at a node or any other point of the wire. Hence a strict 

 comparison of the observed amplitudes with theory is 

 possible. 



It is the aim of this paper to develop the theory so as to 

 explain the facts of observation regarding the amplitude 

 maintained. The details of the experiment are given in the 

 paper cited above, and it will suffice to summarize below 

 the main results, a is the constant factor of the periodic 

 maintaining influence and in the experiment, for the same 

 wire, depends upon the current through the wire and can 

 be kept constant for an indefinite length of time or can be 

 altered at will, n is the natural frequency of the vibrating 

 wire, and can be altered by altering the tension or the length 

 of the wire, It was found that the maintenance started when 

 the tension was slightly greater than that necessary to make 

 n=p, i. e. when p 2 — n 2 was negative. Maintenance continued 

 as tension diminished so as to make n — p and n less than p, 

 i. e. as p 2 — n 2 became zero and as p 2 — n 2 increased positively. 



§ 6 



2 



$ 3 



Fig. 1. 



_^— o-' — ° 



^ ^Ao 1 



— 160 -120 -GO 



0> 



120 



180 



24-0 



360 



(1) When the observed amplitudes are plotted * against 

 the differences of the squares of the forced and the natural 

 frequencies, there is no "peak" or maximum resonance as 

 in the case of the ordinary forced oscillations, but only a 

 continual increase in the amplitude from one end of the 

 range where p 2 — n 2 is negative to the other end of the range 

 where p 2 — n 2 is positive. 



(2) The amplitude increases to a maximum value after 



* Figure 1 of the author's paper cited above. 



400 



